Quantum charges and spacetime topology: The emergence of new superselection sectors

Abstract

In which is developed a new form of superselection sectors of topological origin. By that it is meant a new investigation that includes several extensions of the traditional framework of Doplicher, Haag and Roberts in local quantum theories. At first we generalize the notion of representations of nets of C*-algebras, then we provide a brand new view on selection criteria by adopting one with a strong topological flavour. We prove that it is coherent with the older point of view, hence a clue to a genuine extension. In this light, we extend Roberts' cohomological analysis to the case where 1--cocycles bear non trivial unitary representations of the fundamental group of the spacetime, equivalently of its Cauchy surface in case of global hyperbolicity. A crucial tool is a notion of group von Neumann algebras generated by the 1-cocycles evaluated on loops over fixed regions. One proves that these group von Neumann algebras are localized at the bounded region where loops start and end and to be factorial of finite type I. All that amounts to a new invariant, in a topological sense, which can be defined as the dimension of the factor. We prove that any 1-cocycle can be factorized into a part that contains only the charge content and another where only the topological information is stored. This second part resembles much what in literature are known as geometric phases. Indeed, by the very geometrical origin of the 1-cocycles that we discuss in the paper, they are essential tools in the theory of net bundles, and the topological part is related to their holonomy content. At the end we prove the existence of net representations.

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• A new light on nets of C*-algebras and their representations
• Characteristics, Conal Geometry and Causality in Locally Covariant Field Theory
• Globally hyperbolic spacetimes: slicings, boundaries and counterexamples
• Dynamical locality of the nonminimally coupled scalar field and enlarged algebra of Wick polynomials
• Causal posets, loops and the construction of nets of local algebras for QFT
• Topological features of massive bosons on two dimensional Einstein space-time
• Presheaves of superselection structures in curved spacetimes
• The C(X)-algebra of a net and index theory
• The K-homology of nets of C*-algebras
• QED Representation for the Net of Causal Loops
• Representations of nets of C*-algebras over S^1
• Background potentials and superselection sectors
• Locally covariant quantum field theory and the spin-statistics connection
• Aharonov-Bohm superselection sectors
• Massless scalar free Field in 1+1 dimensions, II: Net Cohomology and Completeness of Superselection Sectors
• Manifold Topology, Observables and Gauge Group
• Topological sectors for Weyl-algebra net in the Einstein cylindrical universe
• $C^{\ast }$-categorical prefactorization algebras for superselection sectors and topological order
• Gerbes over posets and twisted C*-dynamical systems